Question:
Find the value of a, so that the point (3, a) lies on the line 2x − 3y = 5.
Solution:
The point $(3, a)$ lies on the line $2 x-3 y=5$.
If point $(3, a)$ lies on the line $2 x-3 y=5$, then
$2 x-3 y=5$
$\Rightarrow(2 \times 3)-(3 \times a)=5$
$\Rightarrow 6-3 a=5$
$\Rightarrow 3 a=1$
$\Rightarrow a=\frac{1}{3}$
Hence, the value of $a$ is $\frac{1}{3}$.